Question : A wheel with 100 metallic spokes each of 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field. If the resultant magnetic field at that place is 4×10-4T, find the emf induced between the axle and the rim of the wheel. What will be the change in emf induced if the number spokes is doubled.
Doubt by Ananya
Solution :
No. of spokes = 100
Length of each spoke / radius (L) = 0.5 m
frequency (𝛎)
= 120 rev/min
= 120/60 rev/s
= 2 rev/s
Angular frequency (⍵)
= 2π𝛎
= 2×π×2
= 4π rad/s
= 120 rev/min
= 120/60 rev/s
= 2 rev/s
Angular frequency (⍵)
= 2π𝛎
= 2×π×2
= 4π rad/s
Magnetic Field (B) = 4×10-4T
Induced emf between axle and the rim of the wheel is given by
= ½×BL²⍵
= ½×(4×10-4)(0.5)²×4π
= ½×(0.0004)(0.5)²×4π
= ½×(4×10-4)(0.5)²×4π
= ½×(0.0004)(0.5)²×4π
= (0.0004)(0.5)²×2π
= 0.0004×0.25×2×3.14
= 0.0004×0.50×3.14
= 0.0004×0.25×2×3.14
= 0.0004×0.50×3.14
= 0.000628
= 6.28×10-4 V
Change in emf will remain same even if the number of spokes are doubled because each of the spoke is connected in parallel and we know potential in parallel connection is remains same.
